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Optimal reinsurance with expectile

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  • Jun Cai
  • Chengguo Weng

Abstract

In this paper, we study optimal reinsurance treaties that minimize the liability of an insurer. The liability is defined as the actuarial reserve on an insurer’s risk exposure plus the risk margin required for the risk exposure. The risk margin is determined by the risk measure of expectile. Among a general class of reinsurance premium principles, we prove that a two-layer reinsurance treaty is optimal. Furthermore, if a reinsurance premium principle in the class is translation invariant or is the expected value principle, we show that a one-layer reinsurance treaty is optimal. Moreover, we use the expected value premium principle and Wang’s premium principle to demonstrate how the parameters in an optimal reinsurance treaty can be determined explicitly under a given premium principle.

Suggested Citation

  • Jun Cai & Chengguo Weng, 2016. "Optimal reinsurance with expectile," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(7), pages 624-645, August.
    • Handle: RePEc:taf:sactxx:v:2016:y:2016:i:7:p:624-645
    DOI: 10.1080/03461238.2014.994025
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    Cited by:

    1. Ernest Aboagye & Vali Asimit & Tsz Chai Fung & Liang Peng & Qiuqi Wang, 2024. "A Revisit of the Optimal Excess-of-Loss Contract," Papers 2405.00188, arXiv.org.
    2. Cheung, Ka Chun & He, Wanting & Wang, He, 2023. "Multi-constrained optimal reinsurance model from the duality perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 199-214.
    3. Gao, Suhao & Yu, Zhen, 2023. "Parametric expectile regression and its application for premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 242-256.
    4. Tim J. Boonen & Xia Han, 2023. "Optimal insurance with mean-deviation measures," Papers 2312.01813, arXiv.org.

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